In this paper, we investigate the dynamics of small unilamellar vesicles with the aid of neutron spin-echo spectroscopy. The purpose of this investigation is twofold. On the one hand, we investigate the influence of solubilised cosurfactant on the dynamics of the vesicle's surfactant bilayer. On the other hand, the small unilamellar vesicles used here have a size between larger vesicles, with dynamics being well described by the Zilman-Granek model and smaller microemulsion droplets which can be described by the Milner-Safran model. Therefore, we want to elucidate the question, which model is more suitable for the description of the membrane dynamics of small vesicles, where the finite curvature of the bilayer is felt by the contained amphiphilic molecules. This question is of substantial relevance for our understanding of membranes and how their dynamics is affected by curvature, a problem that is also of key importance in a number of biological questions. Our results indicate the even down to vesicle radii of 20 nm the Zilman-Granek model appears to be the more suitable one.